The data analytic scripts and supplemental materials for this project are available at https://github.com/sarhen907/MLM-WLS. This .html provides output from statistical models and graphically represents data in various plots. Individual models may be run in the .rmd, and individual steps for analysis may be navigated through the .rmd tabs.

Data manipulation

Descriptive

Demographics

##  yob           sex               edu1      childincomecompare  adultincome    
##  37:  44   Male  :1983   NoHigherEd:2794   Min.   :1.000      Min.   : 0.003  
##  38: 631   Female:2266   Associates: 116   1st Qu.:3.000      1st Qu.: 4.000  
##  39:3342                 Bachelors : 735   Median :3.000      Median : 6.000  
##  40: 232                 Masters   : 442   Mean   :3.163      Mean   : 7.443  
##                          Doctorate : 162   3rd Qu.:3.000      3rd Qu.: 8.910  
##                                            Max.   :5.000      Max.   :30.000

Summary Tables

## 
## <table style="text-align:center"><caption><strong>Simlarities (WAIS)</strong></caption>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">year</td><td>N</td><td>mean</td><td>sd</td><td>se</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">1992</td><td>4,674</td><td>8.117</td><td>2.681</td><td>0.039</td></tr>
## <tr><td style="text-align:left">2004</td><td>4,456</td><td>6.810</td><td>2.329</td><td>0.035</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr></table>
## 
## <table style="text-align:center"><caption><strong>Categorical Fluency</strong></caption>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">year</td><td>N</td><td>mean</td><td>sd</td><td>se</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">2004</td><td>2,145</td><td>21.392</td><td>6.109</td><td>0.132</td></tr>
## <tr><td style="text-align:left">2011</td><td>2,104</td><td>19.945</td><td>5.937</td><td>0.129</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr></table>
## 
## <table style="text-align:center"><caption><strong>Letter Fluency</strong></caption>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">year</td><td>N</td><td>mean</td><td>sd</td><td>se</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">2004</td><td>3,306</td><td>11.680</td><td>4.272</td><td>0.074</td></tr>
## <tr><td style="text-align:left">2011</td><td>4,203</td><td>11.363</td><td>4.162</td><td>0.064</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr></table>
## 
## <table style="text-align:center"><caption><strong>Immediate Recall</strong></caption>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">year</td><td>N</td><td>mean</td><td>sd</td><td>se</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">2004</td><td>3,560</td><td>6.241</td><td>1.697</td><td>0.028</td></tr>
## <tr><td style="text-align:left">2011</td><td>3,498</td><td>5.553</td><td>1.396</td><td>0.024</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr></table>
## 
## <table style="text-align:center"><caption><strong>Digit Ordering</strong></caption>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">year</td><td>N</td><td>mean</td><td>sd</td><td>se</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr><tr><td style="text-align:left">2004</td><td>3,342</td><td>7.817</td><td>2.461</td><td>0.043</td></tr>
## <tr><td style="text-align:left">2011</td><td>3,373</td><td>7.229</td><td>2.191</td><td>0.038</td></tr>
## <tr><td colspan="5" style="border-bottom: 1px solid black"></td></tr></table>

Correlations between variables

predictors only

Outcome variables

ICC

simscore

## [1] 0.4078702
##     2.5 %    97.5 % 
## 0.3830407 0.4321178
## [1] 1.40787

categorical fluency

## [1] 0.5811758
##     2.5 %    97.5 % 
## 0.5513553 0.6094421
## [1] 1.581176

letter fluency

## [1] 0.5884791
##     2.5 %    97.5 % 
## 0.5653130 0.6105755
## [1] 1.588479

immediate recall

## [1] 0.2409269
##     2.5 %    97.5 % 
## 0.2089275 0.2723645
## [1] 1.240927

digit ordering

## [1] 0.3141478
##     2.5 %    97.5 % 
## 0.2819833 0.3455739
## [1] 1.314148

Similarities

Models

Edu only

SES only

Edu and Income

Final table

Results of Similarities Modeling
  by Time Edu * Year Edu * Sex * Year Income * Year Income * Sex * Year Income * Sex * Edu * Year Child Income * Year Child Income * Sex * Year Child Income * Sex * Edu * Year
(Intercept) 8.12*** 7.51*** 7.35*** 7.52*** 7.37*** 6.91*** 7.72*** 7.83*** 7.58***
  (0.04) (0.04) (0.07) (0.06) (0.10) (0.12) (0.22) (0.32) (0.40)
year2004 -1.31*** -1.27*** -1.23*** -1.23*** -1.15*** -1.08*** -1.28*** -1.13*** -0.81*
  (0.04) (0.04) (0.07) (0.06) (0.09) (0.12) (0.21) (0.30) (0.40)
edu   0.75*** 0.74***     0.87***     0.84***
    (0.03) (0.04)     (0.07)     (0.21)
edu:year2004   -0.06 -0.08     -0.10     -0.31
    (0.03) (0.04)     (0.07)     (0.21)
sexFemale     0.27**   0.25 0.41**   -0.23 -0.07
      (0.09)   (0.13) (0.15)   (0.44) (0.53)
sexFemale:edu     0.06     0.00     0.22
      (0.06)     (0.11)     (0.32)
sexFemale:year2004     -0.07   -0.13 -0.19   -0.27 -0.56
      (0.09)   (0.12) (0.15)   (0.42) (0.54)
sexFemale:edu:year2004     0.04     0.05     0.19
      (0.06)     (0.11)     (0.33)
adultincome       0.08*** 0.09*** 0.06***      
        (0.01) (0.01) (0.01)      
adultincome:year2004       -0.01 -0.02* -0.02      
        (0.01) (0.01) (0.01)      
sexFemale:adultincome         -0.01 -0.01      
          (0.01) (0.02)      
sexFemale:adultincome:year2004         0.01 0.02      
          (0.01) (0.02)      
adultincome:edu           -0.02**      
            (0.01)      
sexFemale:adultincome:edu           0.00      
            (0.01)      
adultincome:edu:year2004           0.00      
            (0.01)      
sexFemale:adultincome:edu:year2004           -0.00      
            (0.01)      
childincomecompare             0.13 0.09 -0.07
              (0.07) (0.10) (0.12)
childincomecompare:year2004             -0.01 -0.05 -0.13
              (0.07) (0.09) (0.13)
sexFemale:childincomecompare               0.08 0.11
                (0.14) (0.17)
sexFemale:childincomecompare:year2004               0.08 0.16
                (0.13) (0.17)
childincomecompare:edu                 -0.03
                  (0.06)
sexFemale:childincomecompare:edu                 -0.05
                  (0.10)
childincomecompare:edu:year2004                 0.07
                  (0.06)
sexFemale:childincomecompare:edu:year2004                 -0.05
                  (0.10)
AIC 41343.67 40523.41 40504.01 41171.72 41174.24 40470.82 41342.91 41349.06 40513.61
Log Likelihood -20666.84 -20254.71 -20241.00 -20578.86 -20576.12 -20216.41 -20664.46 -20663.53 -20237.81
Num. obs. 9130 9130 9130 9130 9130 9130 9130 9130 9130
Num. groups: personid 4674 4674 4674 4674 4674 4674 4674 4674 4674
Var: personid (Intercept) 7.19 6.35 6.33 6.98 6.97 6.28 7.18 7.18 6.32
Var: personid year2004 6.26 6.26 6.26 6.26 6.25 6.26 6.26 6.26 6.26
p < 0.001; p < 0.01; p < 0.05

Printed Table to a word doc

Plots

Adult variables

Child Variables

Categorical Fluency

Models

Edu only

Edu and Income

Final table

Results of Categorical Fluency Modeling
  by Time Edu * Year Edu * Sex * Year Income * Year Income * Sex * Year Income * Sex * Edu * Year Child Income * Year Child Income * Sex * Year Child Income * Sex * Edu * Year
(Intercept) 21.39*** 20.35*** 19.08*** 7.52*** 7.37*** 18.49*** 7.72*** 7.83*** 20.48***
  (0.13) (0.15) (0.23) (0.06) (0.10) (0.40) (0.22) (0.32) (1.36)
year2011 -1.49*** -1.18*** -1.29***     -1.39***     -1.27
  (0.12) (0.14) (0.22)     (0.38)     (1.28)
edu   1.24*** 1.27***     1.45***     0.58
    (0.10) (0.13)     (0.24)     (0.71)
edu:year2011   -0.37*** -0.26*     -0.10     0.22
    (0.09) (0.12)     (0.23)     (0.67)
sexFemale     2.15***   0.25 2.47***   -0.23 0.09
      (0.30)   (0.13) (0.52)   (0.44) (1.80)
sexFemale:edu     0.28     0.08     1.35
      (0.20)     (0.35)     (1.09)
sexFemale:year2011     0.23     0.27     0.16
      (0.29)     (0.49)     (1.70)
sexFemale:edu:year2011     -0.28     -0.35     -1.06
      (0.19)     (0.34)     (1.04)
adultincome       0.08*** 0.09*** 0.08      
        (0.01) (0.01) (0.05)      
year2004       -1.23*** -1.15***   -1.28*** -1.13***  
        (0.06) (0.09)   (0.21) (0.30)  
adultincome:year2004       -0.01 -0.02*        
        (0.01) (0.01)        
sexFemale:adultincome         -0.01 -0.04      
          (0.01) (0.07)      
sexFemale:year2004         -0.13     -0.27  
          (0.12)     (0.42)  
sexFemale:adultincome:year2004         0.01        
          (0.01)        
adultincome:edu           -0.03      
            (0.02)      
adultincome:year2011           0.01      
            (0.04)      
sexFemale:adultincome:edu           0.02      
            (0.03)      
sexFemale:adultincome:year2011           -0.00      
            (0.06)      
adultincome:edu:year2011           -0.01      
            (0.02)      
sexFemale:adultincome:edu:year2011           0.00      
            (0.03)      
childincomecompare             0.13 0.09 -0.45
              (0.07) (0.10) (0.43)
childincomecompare:year2004             -0.01 -0.05  
              (0.07) (0.09)  
sexFemale:childincomecompare               0.08 0.66
                (0.14) (0.57)
sexFemale:childincomecompare:year2004               0.08  
                (0.13)  
childincomecompare:edu                 0.21
                  (0.22)
childincomecompare:year2011                 -0.01
                  (0.40)
sexFemale:childincomecompare:edu                 -0.34
                  (0.33)
sexFemale:childincomecompare:year2011                 0.02
                  (0.54)
childincomecompare:edu:year2011                 -0.14
                  (0.20)
sexFemale:childincomecompare:edu:year2011                 0.24
                  (0.32)
AIC 26431.86 26285.03 26176.22 41171.72 41174.24 26184.05 41342.91 41349.06 26189.07
Log Likelihood -13210.93 -13135.52 -13077.11 -20578.86 -20576.12 -13073.02 -20664.46 -20663.53 -13075.53
Num. obs. 4249 4249 4249 9130 9130 4249 9130 9130 4249
Num. groups: personid 2280 2280 2280 4674 4674 2280 4674 4674 2280
Var: personid (Intercept) 37.42 35.01 33.58 6.98 6.97 33.50 7.18 7.18 33.55
Var: personid year2011 28.58 28.35 28.33     28.31     28.32
Var: personid year2004       6.26 6.25   6.26 6.26  
p < 0.001; p < 0.01; p < 0.05

printed table for .doc

Plots

Adult variables

no higher ed vs higher ed

Child Variables

no higher ed vs higher ed

Letter Fluency

Models

Edu only

add gender

SES only

adult income

Edu and Income

Final table

Results of Letter Fluency Modeling
  by Time Edu * Year Edu * Sex * Year Income * Year Income * Sex * Year Income * Sex * Edu * Year Child Income * Year Child Income * Sex * Year Child Income * Sex * Edu * Year
(Intercept) 11.63*** 11.07*** 10.23*** 10.93*** 10.14*** 9.64*** 11.79*** 11.64*** 11.97***
  (0.07) (0.08) (0.13) (0.12) (0.18) (0.22) (0.40) (0.57) (0.77)
year2011 -0.31*** -0.37*** -0.39** -0.24* -0.20 -0.28 -0.69 -0.55 -0.47
  (0.07) (0.08) (0.12) (0.11) (0.17) (0.22) (0.37) (0.54) (0.74)
edu   0.68*** 0.78***     0.90***     0.46
    (0.06) (0.07)     (0.13)     (0.40)
edu:year2011   0.08 0.07     0.12     -0.01
    (0.05) (0.07)     (0.13)     (0.38)
sexFemale     1.41***   1.24*** 1.56***   0.05 0.67
      (0.17)   (0.23) (0.29)   (0.79) (1.01)
sexFemale:edu     -0.04     -0.27     -0.74
      (0.11)     (0.20)     (0.60)
sexFemale:year2011     0.03   -0.06 0.07   -0.23 -0.04
      (0.16)   (0.22) (0.28)   (0.75) (0.98)
sexFemale:edu:year2011     0.04     -0.11     -0.11
      (0.11)     (0.19)     (0.58)
adultincome       0.09*** 0.11*** 0.09***      
        (0.01) (0.02) (0.03)      
adultincome:year2011       -0.01 -0.01 -0.02      
        (0.01) (0.02) (0.03)      
sexFemale:adultincome         0.00 -0.01      
          (0.03) (0.04)      
sexFemale:adultincome:year2011         0.01 -0.01      
          (0.02) (0.04)      
adultincome:edu           -0.02      
            (0.01)      
sexFemale:adultincome:edu           0.02      
            (0.02)      
adultincome:edu:year2011           -0.00      
            (0.01)      
sexFemale:adultincome:edu:year2011           0.02      
            (0.02)      
childincomecompare             -0.05 -0.19 -0.56*
              (0.12) (0.18) (0.24)
childincomecompare:year2011             0.12 0.07 0.03
              (0.12) (0.17) (0.23)
sexFemale:childincomecompare               0.32 0.23
                (0.25) (0.32)
sexFemale:childincomecompare:year2011               0.08 0.02
                (0.23) (0.31)
childincomecompare:edu                 0.11
                  (0.12)
sexFemale:childincomecompare:edu                 0.21
                  (0.18)
childincomecompare:edu:year2011                 0.02
                  (0.12)
sexFemale:childincomecompare:edu:year2011                 0.04
                  (0.18)
AIC 41619.77 41378.09 41231.05 41549.11 41439.25 41208.80 41622.64 41538.52 41227.38
Log Likelihood -20804.88 -20682.05 -20604.53 -20767.56 -20708.62 -20585.40 -20804.32 -20758.26 -20594.69
Num. obs. 7509 7509 7509 7509 7509 7509 7509 7509 7509
Num. groups: personid 4504 4504 4504 4504 4504 4504 4504 4504 4504
Var: personid (Intercept) 18.32 17.62 17.16 18.01 17.62 17.00 18.32 18.03 17.11
Var: personid year2011 14.54 14.53 14.52 14.56 14.57 14.54 14.54 14.53 14.52
p < 0.001; p < 0.01; p < 0.05

printed table to word doc

Plots

#### Adult variables

Child Variables

Immediate Recall

Models

Edu only

Adding edu

add gender

Break down the 3 way interaction

edu*year in just females

edu*year in just males

SES only

Edu and Income

Final table

Results of Immediate Recall Modeling
  by Time Edu * Year Edu * Sex * Year Income * Year Income * Sex * Year Income * Sex * Edu * Year Child Income * Year Child Income * Sex * Year Child Income * Sex * Edu * Year
(Intercept) 6.24*** 6.10*** 5.47*** 6.07*** 5.48*** 5.30*** 6.03*** 5.29*** 5.18***
  (0.03) (0.03) (0.05) (0.05) (0.07) (0.09) (0.16) (0.22) (0.30)
year2011 -0.69*** -0.71*** -0.48*** -0.68*** -0.45*** -0.44*** -0.62*** -0.18 0.09
  (0.03) (0.04) (0.06) (0.05) (0.08) (0.10) (0.17) (0.25) (0.34)
edu   0.17*** 0.31***     0.37***     0.38*
    (0.02) (0.03)     (0.05)     (0.16)
edu:year2011   0.02 -0.06     -0.05     -0.25
    (0.03) (0.03)     (0.06)     (0.18)
sexFemale     1.08***   0.94*** 1.02***   1.20*** 1.08**
      (0.07)   (0.09) (0.11)   (0.31) (0.40)
sexFemale:edu     -0.20***     -0.19*     0.00
      (0.04)     (0.08)     (0.24)
sexFemale:year2011     -0.39***   -0.39*** -0.33*   -0.79* -0.83
      (0.08)   (0.10) (0.13)   (0.35) (0.46)
sexFemale:edu:year2011     0.17**     0.05     0.10
      (0.05)     (0.09)     (0.27)
adultincome       0.02*** 0.04*** 0.02*      
        (0.01) (0.01) (0.01)      
adultincome:year2011       -0.00 -0.01 -0.01      
        (0.01) (0.01) (0.01)      
sexFemale:adultincome         -0.01 0.01      
          (0.01) (0.01)      
sexFemale:adultincome:year2011         0.02 -0.01      
          (0.01) (0.02)      
adultincome:edu           -0.01      
            (0.00)      
sexFemale:adultincome:edu           -0.00      
            (0.01)      
adultincome:edu:year2011           -0.00      
            (0.01)      
sexFemale:adultincome:edu:year2011           0.01      
            (0.01)      
childincomecompare             0.07 0.16* 0.09
              (0.05) (0.07) (0.10)
childincomecompare:year2011             -0.02 -0.12 -0.18
              (0.05) (0.08) (0.11)
sexFemale:childincomecompare               -0.11 0.00
                (0.10) (0.13)
sexFemale:childincomecompare:year2011               0.17 0.14
                (0.11) (0.14)
childincomecompare:edu                 -0.02
                  (0.05)
sexFemale:childincomecompare:edu                 -0.06
                  (0.07)
childincomecompare:edu:year2011                 0.06
                  (0.05)
sexFemale:childincomecompare:edu:year2011                 0.02
                  (0.08)
AIC 25800.63 25673.98 25288.29 25770.23 25441.75 25269.10 25802.23 25513.05 25298.13
Log Likelihood -12895.31 -12829.99 -12633.14 -12878.12 -12709.87 -12615.55 -12894.11 -12745.52 -12630.07
Num. obs. 7058 7058 7058 7058 7058 7058 7058 7058 7058
Num. groups: personid 3634 3634 3634 3634 3634 3634 3634 3634 3634
Var: personid (Intercept) 2.88 2.83 2.62 2.86 2.67 2.60 2.88 2.70 2.61
Var: personid year2011 3.37 3.37 3.34 3.37 3.35 3.34 3.37 3.35 3.34
p < 0.001; p < 0.01; p < 0.05

printed table to doc

Plots

#### Adult variables

Child Variables

Digit Ordering

Models

Edu only

SES only

Edu and Income

Final table

Results of Digit Ordering Modeling
  by Time Edu * Year Edu * Sex * Year Income * Year Income * Sex * Year Income * Sex * Edu * Year Child Income * Year Child Income * Sex * Year Child Income * Sex * Edu * Year
(Intercept) 7.79*** 7.58*** 7.20*** 7.57*** 7.18*** 6.98*** 7.97*** 7.35*** 7.25***
  (0.04) (0.05) (0.08) (0.07) (0.11) (0.14) (0.24) (0.34) (0.47)
year2011 -0.57*** -0.58*** -0.43*** -0.53*** -0.46*** -0.43** -0.69** -0.33 0.09
  (0.05) (0.06) (0.09) (0.08) (0.12) (0.15) (0.26) (0.38) (0.53)
edu   0.25*** 0.34***     0.38***     0.39
    (0.03) (0.05)     (0.08)     (0.24)
edu:year2011   0.01 0.01     -0.02     -0.29
    (0.04) (0.05)     (0.09)     (0.27)
sexFemale     0.66***   0.63*** 0.65***   1.06* 1.15
      (0.10)   (0.14) (0.18)   (0.47) (0.62)
sexFemale:edu     -0.13     -0.05     -0.13
      (0.07)     (0.12)     (0.37)
sexFemale:year2011     -0.25*   -0.07 0.02   -0.60 -0.69
      (0.12)   (0.16) (0.20)   (0.53) (0.70)
sexFemale:edu:year2011     -0.04     -0.11     -0.12
      (0.08)     (0.13)     (0.41)
adultincome       0.03*** 0.04*** 0.03      
        (0.01) (0.01) (0.02)      
adultincome:year2011       -0.01 0.00 -0.00      
        (0.01) (0.01) (0.02)      
sexFemale:adultincome         -0.02 0.01      
          (0.02) (0.02)      
sexFemale:adultincome:year2011         -0.03 -0.04      
          (0.02) (0.02)      
adultincome:edu           -0.01      
            (0.01)      
sexFemale:adultincome:edu           -0.01      
            (0.01)      
adultincome:edu:year2011           0.00      
            (0.01)      
sexFemale:adultincome:edu:year2011           0.01      
            (0.01)      
childincomecompare             -0.06 0.06 -0.02
              (0.07) (0.11) (0.15)
childincomecompare:year2011             0.04 -0.03 -0.17
              (0.08) (0.12) (0.17)
sexFemale:childincomecompare               -0.20 -0.16
                (0.15) (0.20)
sexFemale:childincomecompare:year2011               0.10 0.14
                (0.16) (0.22)
childincomecompare:edu                 -0.02
                  (0.07)
sexFemale:childincomecompare:edu                 0.00
                  (0.11)
childincomecompare:edu:year2011                 0.09
                  (0.08)
sexFemale:childincomecompare:edu:year2011                 0.02
                  (0.13)
AIC 30008.62 29913.94 29867.41 29990.89 29950.21 29866.80 30012.06 29990.53 29875.07
Log Likelihood -14999.31 -14949.97 -14922.70 -14988.44 -14964.11 -14914.40 -14999.03 -14984.26 -14918.53
Num. obs. 6715 6715 6715 6715 6715 6715 6715 6715 6715
Num. groups: personid 3587 3587 3587 3587 3587 3587 3587 3587 3587
Var: personid (Intercept) 6.06 5.96 5.88 6.03 5.97 5.87 6.06 6.00 5.88
Var: personid year2011 7.25 7.25 7.22 7.24 7.22 7.21 7.25 7.23 7.22
p < 0.001; p < 0.01; p < 0.05

Printed table

Plots

Adult variables

Child Variables